论文标题
广义Lyapunov指数上的量子界限
Quantum bounds on the generalized Lyapunov exponents
论文作者
论文摘要
我们讨论了广义的量子Lyapunov指数$ L_Q $，该指数是根据平方换向器的力量增长率定义的。它们可能与换向器光谱的适当定义的热力学极限有关，该频谱扮演着大型偏差函数的作用，该函数是通过Legendre变换从指数$ L_Q $获得的。我们表明，由于文献中已经讨论的那样，由于波动的定理，这种指数遵守了与混乱的一般性约束。较大的$ Q $的边界实际上更强，对混乱特性的巨大偏差限制。我们在无限温度下的发现是通过对量子混乱的范式模型的踢顶的数值研究来体现的。
We discuss the generalized quantum Lyapunov exponents $L_q$, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents $L_q$ via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger $q$ are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.
